Re: "quantum mechanics and experience"--non separability

From: Bill Hobba (bhobba_at_rubbish.net.au)
Date: 10/17/04 

Date: Sun, 17 Oct 2004 01:16:18 GMT

<richardconers@yahoo.com> wrote in message
news:9543a42e.0410161600.74d67073@posting.google.com...
> I'm reading "Quantum mechanics and experience". It's starting to sink
> in, and I hope I can use this formum to clarify some points as I go
> along (I finished reading it, but I'm reading it a second time because
> there's no way I get it entirely in the first round <g>.)
>
> My big hang-up so far is understanding non-locality/non-separability
> of 2 particle states.

There is not much to it really - except is it is described by the one state
that contains the information of two particles - this leads to strange
correlations like the so called EPR paradox (which is really not a paradox).
Different interpretations handle what this means differently.

> Albert doesn't explain how such a state comes
> about in the first place.

It is just how QM works - the same as any theory.

> Can I assume that all combinations of 2
> particles at a time are NOT in a non-separable state?

Sure

> Then what puts them into that state?

The way they were created eg for photons in the EPR experiment multiple
photons were emitted from the same source.

> And what causes the end of non-separability
> (i.e., separate reactions of the particles independent of the changes
> going on in the other particle)?

Observation. Now exactly how an observation does that is the 64 million
dollar question of QM - each interpretation handles it differently eg the
consistent history intepretion I am currently investigating tries to avoid
the concept entirely http://quantum.phys.cmu.edu/histories.html.

> And what properties of the 2
> particles are non-separable? (surely not all properties, i.e.,
> location <g>).

I can not think of any that, in principle, are not - it all depends on how
the state was prepared i.e. the total experimental setup in the Copenhagen
interpretation.

>
> Also, I don't understand why Albert makes such a big deal out of
> non-locality. If two particles are in a "non-separable state" where
> the color of A is opposite the color of B (A+B = 0) is the quantum
> state of the two particle system, then non-locality seems to follow
> logically.
>

What it has to do with is your view of the world. Their are a myriad of
different interpretations of QM - study them and pick the one you like.

>
> In this state neither A's color nor B's color is determined, just the
> state of the two particle system. So if A is then measured, A-B is
> still undetermined because B has not been measured yet. When B is
> finally measured, it will turn out to be "minus A or the opposite of
> A", unless something is done to change the two particle system, which
> meausring alone won't do, since A-B is already in a determined state.
> So B, at the time of measuring of A, is still undetermined, but there
> is no way (I assume) to confirm that B is undetermined without
> measuring it. As soon as you measure B, it must be "minus A" per the
> 2 particle system state.
>
> If the above is true, nothing in that description calls for any
> "direct, physical" contact between A and B, so non-locality is
> inherent in having something called a "non-separable" state. You
> don't even need Bell's theorem to conclude this, do you?

That is interpretation dependant. What Bells theorem shows is if the
measured properties depend of some variables that exist out their
independent of our observing them then they must be non local influences
connecting them. The out is that such variables do not necessarily have to
exist. You may wish to acquaint yourself with the Kochen-Specker Theorem
http://plato.stanford.edu/entries/kochen-specker/.

>
> I raise this question because this non-separability seems to me to be
> very, very much different from incompatible properties of a one
> particle system. It seems like quantum mechanics is asserting right
> from the start that there are pairs of properties of a single particle
> which are 100% incompatible. This seems to be inherent in the
> physical makeup of the universe.
>
> In contrast, I don't think Albert makes explicit under what
> circumstances non-separability of two particle systems obtains. Is he
> saying that non-separability is inherent in all two particle pairs,
> just like incompatibility is inherent in pairs of properties of one
> particle systems? Even so, that wouldn't mean that all 2 particle
> pairs are in a non-separable state, since only specific pairs of
> properties of a one particle state are incompatible, not all pairs of
> properties.

It is just like many other properties of quantum systems - it is not a
property until it is measured. In EPR type experiments when we measure the
spin of one photon it immediately tells us the spin of the other - exactly
what this means depends on what interpretation you hold to.

>
> So that leads me back to the question of what generates
> non-separability of two particle systems--and which properties become
> non-separable under those circumstances (hopefully it doesn't mean
> that all properties are non-separable in that state)?
>
> Thank you for your explanation(s)!!!

Bill

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